Representative Lamar Smith of Texas, the senior Republican on the House Judiciary Committee, said the Smadi case “points to a real need for an entry and exit system if we are serious about reducing illegal immigration.”

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Senator Charles E. Schumer, Democrat of New York and chairman of the Judiciary Committee’s subcommittee on immigration, said he would try to steer money from the economic stimulus program to build an exit monitoring system.

Since the Sept. 11 attacks, immigration authorities, with more than $1 billion from Congress, have greatly improved and expanded their systems to monitor foreigners when they arrive. But despite several Congressional authorizations, there are no biometric inspections or a systematic follow-up to confirm that foreign visitors have departed.

Homeland security officials caution that universal exit monitoring is a daunting and costly goal, mainly because of the nation’s long and busy land borders, with more than one million crossings every day. The wrong exit plan, they said, could clog trade, disrupt border cities and overwhelm immigration agencies with information they could not effectively use.

Since 2004, homeland security officials have put systems in place to check all foreigners as they arrive, whether by air, sea or land. Customs officers now take fingerprints and digital photographs of visitors from most countries, instantly comparing them against law enforcement watch list databases. (Canadians and Mexicans with special border-crossing cards are exempt from those checks.)

But homeland security officials said that a series of pilot programs since 2004 had failed to yield an exit monitoring system that would work for the whole nation. They have not yet found technology to support speedy exit inspections at land borders. And airlines balked at an effort last year by the Bush administration to make them responsible for taking fingerprints and photographs of departing foreigners.

The current system relies on departing foreigners to turn in a paper stub when they leave.

Last year, official figures show, 39 million foreign travelers were admitted on temporary visas like Mr. Smadi’s. Based on the paper stubs, homeland security officials said, they confirmed the departure of 92.5 percent of them. Most of the remaining visitors did depart, officials said, but failed to check out because they did not know how to do so. But more than 200,000 of them are believed to have overstayed intentionally.

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Immigration authorities have put in place a separate system for keeping track of foreigners who, unlike Mr. Smadi, come on student visas. That system has proved effective at confirming that the students have stayed in school and do not overstay their visas, officials said.

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Immigration analysts said that given the difficulties of enforcing the United States’ vast borders, it remains primarily up to law enforcement officials to thwart terrorism suspects who do not have records that would draw scrutiny before they enter the United States.

“You can’t ask the immigration system to do everything,” said Doris Meissner, a senior fellow at the Migration Policy Institute, a research center in Washington, and a former commissioner of the immigration service. “This is an example of how changes in law enforcement priorities and techniques since Sept. 11 actually got to where they should be.”

Mr. Smadi, like many tourists who overstay visas, was able to fade easily into society and encountered few barriers to starting a life here, according to court documents and people who know him. He enrolled in high school, obtained a California identification card, landed jobs in two states and rented a string of apartments and houses. He bought at least two used cars, and even procured a handgun and ammunition.

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Mr. Smadi’s arrest on Sept. 24 for the attempted bombing was not his first encounter with American law enforcement. Two weeks earlier, a sheriff’s deputy in Ellis County, Tex., pulled him over for a broken tail light just north of the town of Italy, then arrested him for driving without a license or insurance.

When the deputy checked his identity, Mr. Smadi’s name showed up on a watch list by the Federal Bureau of Investigation, which was already investigating him. But the background check turned up no immigration record. The deputy called the F.B.I. and was told there was no outstanding arrest warrant for Mr. Smadi. So on the evening of Sept. 11, Mr. Smadi paid a $550 fine and walked out of the county jail.

“There was nothing to indicate to us that this person was currently in the States illegally,” said Chief Deputy Dennis Brearley.

Mr. Smadi had come to the United States from Jordan in early 2007 on a six-month tourist visa, immigration officials say.

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For a few weeks he stayed in San Jose, Calif., with Hana Elrabodi, a retired Jordanian businessman who knew his family, according to Mr. Elrabodi’s wife, Temina. Though Mr. Smadi was not authorized to work, he found a job at a local restaurant. In late March, Mr. Smadi obtained a California identification card using Mr. Elrabodi’s address.

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In October 2007, Mr. Smadi moved into an apartment in Santa Clara with his younger brother, Hussein Smadi, and another man he identified as his cousin, according to the manager of the apartment complex, Joe Redzovic. Mr. Smadi took another job, in a falafel restaurant, and in the winter he briefly enrolled in the Santa Clara High School.

After a fire gutted his Santa Clara apartment, Mr. Smadi moved to Dallas. Though his visa had expired by April 2008, he landed a job working behind the counter at Texas Best Smokehouse in Italy, Tex., about 45 miles from Dallas. He rented a bungalow nearby, using his California identification and passing a criminal background check, said his former landlord, David South.

Three months later, Mr. Smadi married one of his co-workers, Rosalinda Duron. They separated in the fall of 2008 after only three months, Ms. Duron said.

Investigators have found no evidence that Mr. Smadi, during his first year in the United States, openly espoused Islamic fundamentalism. Neither have they found any evidence that he received terrorist training abroad or came to the United States intending to commit a terrorist act, said Mark White, a spokesman for the F.B.I. in Dallas.

But by the spring of 2008, he caught the attention of the F.B.I. by posting incendiary remarks about wanting to kill Americans on Jihadist Web sites. Over the summer, he met with agents posing as members of Al Qaeda and planned to bomb the Fountain Place office building in downtown Dallas, according to an indictment unsealed on Thursday.

His arrest on terrorism charges came after he parked a truck that he had been told was carrying explosives in the building’s underground garage, according to court documents.

When the F.B.I. later searched his residence, they found a Beretta 9 millimeter pistol and a box of ammunition, along with his passport and the expired visa, the court documents show.